Thanks Bill, it works!
As for my data being weird, well<grin>, it doesn't seem it to me! It
consists of measurements that are taken over as close to a perfect grid as
possible, but likely rotated and certainly with many gaps and offsets due to
physical obstructions in the field. As for the larger sizes, I was enjoying
Curtis's DelaunayFast until I started getting triangulation errors.
I worry when you mention that co-linear points cause problems, because
almost all of my data is similarly co-linear, although often not orthogonal
to the axes. That invites my implementing my own triangulation and using a
CustomDelaunay that exploits this co-linear tendency, but that doesn't seem
trivial even in my near-gridded cases, and I still have to support the
general case. I was hoping that in the medium-term I could use well-known
algorithms _that_work_ even if they're imperfect: I'm not terribly fussy
how equilateral my triangles are, but I do care that the coverage is
complete and non-overlapping so that interpolation can work. Can none of
the Delaunay algorithms guarantee this?
And Curtis, thanks for the DelaunayFast. Unfortunately, I'm getting a fair
number of "Delaunay.finish_triang: error in triangulation!" exceptions.
But fortunately it's fast enough that I can always try it first!
My apologies for the large attachment, I just never succeeded in reproducing
the problem with a smaller dataset. It's just as well that it didn't make
it to the list. I guess I should've written the data in binary form instead
of ascii.
Thanks again for your help!
Ian